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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Removing point singularities of Riemannian manifolds

Authors: P. D. Smith and Deane Yang
Journal: Trans. Amer. Math. Soc. 333 (1992), 203-219
MSC: Primary 53C21; Secondary 53C22
MathSciNet review: 1052910
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Abstract: We study the behavior of geodesics passing through a point singularity of a Riemannian manifold. In particular, we show that if the curvature does not blow up too rapidly near the singularity, then the singularity is at worst an orbifold singularity. The idea is to construct the exponential map centered at a singularity. Since there is no tangent space at the singularity, a surrogate is needed. We show that the vector space of radially parallel vector fields is well defined and that there is a correspondence between unit radially parallel vector fields and geodesics emanating from the singular point.

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PII: S 0002-9947(1992)1052910-2
Article copyright: © Copyright 1992 American Mathematical Society